## spatial statistics

##### AM-25 - Bayesian methods
• Define “prior and posterior distributions” and “Markov-Chain Monte Carlo”
• Explain how the Bayesian perspective is a unified framework from which to view uncertainty
• Compare and contrast Bayesian methods and classical “frequentist” statistical methods
##### AM-24 - Outliers
• Explain how outliers affect the results of analyses
• Explain how the following techniques can be used to examine outliers: tabulation, histograms, box plots, correlation analysis, scatter plots, local statistics
##### AM-23 - Local measures of spatial association
• Describe the effect of non-stationarity on local indices of spatial association
• Decompose Moran’s I and Geary’s c into local measures of spatial association
• Compute the Gi and Gi* statistics
• Explain how geographically weighted regression provides a local measure of spatial association
• Explain how a weights matrix can be used to convert any classical statistic into a local measure of spatial association
• Compare and contrast global and local statistics and their uses
##### AM-22 - Global measures of spatial association
• Describe the effect of the assumption of stationarity on global measures of spatial association
• Justify, compute, and test the significance of the join count statistic for a pattern of objects
• Compute the K function
• Explain how a statistic that is based on combining all the spatial data and returning a single summary value or two can be useful in understanding broad spatial trends
• Compute measures of overall dispersion and clustering of point datasets using nearest neighbor distance statistics
• Compute Moran’s I and Geary’s c for patterns of attribute data measured on interval/ratio scales
• Explain how the K function provides a scale-dependent measure of dispersion
##### AM-21 - The spatial weights matrix
• Explain how different types of spatial weights matrices are defined and calculated
• Discuss the appropriateness of different types of spatial weights matrices for various problems
• Construct a spatial weights matrix for lattice, point, and area patterns
• Explain the rationale used for each type of spatial weights matrix
##### AM-20 - Stochastic processes
• List the two basic assumptions of the purely random process
• Exemplify non-stationarity involving first and second order effects
• Differentiate between isotropic and anisotropic processes
• Discuss the theory leading to the assumption of intrinsic stationarity
• Outline the logic behind the derivation of long run expected outcomes of the independent random process using quadrat counts
• Exemplify deterministic and spatial stochastic processes
• Justify the stochastic process approach to spatial statistical analysis
##### AM-19 - Exploratory data analysis (EDA)
• Describe the statistical characteristics of a set of spatial data using a variety of graphs and plots (including scatterplots, histograms, boxplots, q–q plots)
• Select the appropriate statistical methods for the analysis of given spatial datasets by first exploring them using graphic methods
##### FC-37 - Spatial Autocorrelation

The scientific term spatial autocorrelation describes Tobler’s first law of geography: everything is related to everything else, but nearby things are more related than distant things. Spatial autocorrelation has a:

• past characterized by scientists’ non-verbal awareness of it, followed by its formalization;
• present typified by its dissemination across numerous disciplines, its explication, its visualization, and its extension to non-normal data; and
• an anticipated future in which it becomes a standard in data analytic computer software packages, as well as a routinely considered feature of space-time data and in spatial optimization practice.

Positive spatial autocorrelation constitutes the focal point of its past and present; one expectation is that negative spatial autocorrelation will become a focal point of its future.

##### AM-25 - Bayesian methods
• Define “prior and posterior distributions” and “Markov-Chain Monte Carlo”
• Explain how the Bayesian perspective is a unified framework from which to view uncertainty
• Compare and contrast Bayesian methods and classical “frequentist” statistical methods
##### AM-24 - Outliers
• Explain how outliers affect the results of analyses
• Explain how the following techniques can be used to examine outliers: tabulation, histograms, box plots, correlation analysis, scatter plots, local statistics